His first play Bullfight starring Hurd Hatfield opened off Broadway in 1954. It was followed by The Champagne Complex the following year. His play The Lovers (1956), starring Joanne Woodward, was later filmed as The War Lord (1965). He wrote the Broadway comedy The Marriage-Go-Round (1956), which he adapted to the screen, and produced, as a starring vehicle for Susan Hayward, which was released in 1961. He wrote the screenplay for the film The Left Handed Gun (1958) directed by Arthur Penn and starring Paul Newman.

Other films which Stevens produced, and directed and wrote included Hero's Island (1962) starring James Mason, and Private Property (1960) starring Corey Allen, Warren Oates and his then-wife Kate Manx. In television, he created the series The Outer Limits, which he supervised as executive Producer and wrote or directed a handful of episodes. He also directed the feature film Incubus (1966).

He was Writer, Director and executive Producer of the pilot film and major episodes of It Takes a Thief & McCloud and wrote & produced installments for the series The Invisible Man and Buck Rogers in the 25th Century (which he co-developed with Glen A. Larson). He also produced the first-season Tony Franciosa episodes of The Name of the Game and the short-lived 1972–73 NBC science fiction series Search. Although only credited as supervising Producer of "Saga of a Star-World" (the 1978 pilot episode of the Larson-produced Battlestar Galactica), Director Alan J. Levi has alleged that "Stevens wrote the original script. Leslie was one of my best friends. I do know that Leslie had told me at one time way before he ever got into the script that he had this great idea for a script that he was going to take to Glen Larson and talk about."

Stevens also wrote for the revival show of The Outer Limits between 1996 and 1997.

Stevens died from complications of an emergency angioplasty in 1998 in Los Angeles, California at the age of 74.

Stevens's contributions to the New Age Movement, and its relationships to The Outer Limits are discussed in the book Taoism for Dummies (John Wiley and Sons Canada, 2013).

There is nothing wrong with being a hack Writer. I would point with pride to the inspired hacking of Shakespeare, Michelangelo—you can go through a big list.
As a Playwright, I achieved the rank of night clerk in a hotel at 22, night-ward attendant in a New York psychiatric hospital at 25 and the exalted status of copy boy for Time magazine at 28. These jobs paid my room rent while I was writing plays.